feat(tabs): draw lineage lines as one tree for the selected tab's family

Lineage lines used to draw one glowing dashed bezier per parent/child pair,
hanging below the tab strip, for every family at once. With a parent on row 3
of a wrapped strip and ten children below it, the curves crossed every lower
row's tab names and ran through the terminal text.

- One rounded orthogonal tree per spawning tab: every route starts at the
  parent, so siblings share a trunk. 1.5px, solid, 1px dark outline; only a
  working child's branch is dashed.
- Routes run only through the gaps between tab rows, joined by a spine left of
  every row (computeLineageTree/computeLineageRows in constants.js), so they
  never cross a tab or reach the terminal. The vertical rail gets the same tree
  on its existing left track.
- Only the selected tab's family is drawn (what it spawned, plus its parent and
  siblings). Selection redraws, and the strip's size transitionend redraws once
  more, since the active tab widens for ~150ms after the selection redraw.
- The routing room is reserved by .session-tabs.lineage-tree, keyed on whether
  any lineage exists, never on the selection, so a tab switch never resizes the
  header or the PTY.
- Colours stay per spawning tab, now claimed in strip order for every family so
  selection order never decides who gets the skin blue.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

docs/architecture-invariants.md

@@ -175,15 +175,19 @@ Further detail: `resumeHistorySession()` is what sends `codexConfig.resumeSessio
 
 **Resolved, not trusted** (`resolveParentSessionId()`, route-helpers.ts): exact id first, then a UNIQUE prefix of ≥8 chars (ids reach agents truncated — mux names and a Docker export's `$CODEMAN_SESSION_ID` both carry 8), and an ambiguous prefix resolves to NOTHING rather than to a guess. The parent must be a live session the caller can already see (`canAccessOwned`) AND carry the same owner as the session being created, so a multi-user caller cannot staple their session under someone else's tab. ⚠️ **Everything unresolvable is DROPPED, never a 400**: a stale id from a cached skill preamble must cost a decorative line, not a worker. ⚠️ It is decoration at every layer — never an ownership, permission or lifecycle signal; a child outlives its parent, and the Session ctor refuses a self-parent (reachable only via recovery, where both values come off disk). It rides `toState()` into `session_created` / `session_updated`, so there is **no new SSE event**, and `server.ts`'s recovery path restores it so lineage survives a restart.
 
-**Rendering is an additional LAYER, not a second pass** (`session-lineage.js`, loadorder 15.6): `_updateConnectionLinesImmediate()` (subagent-windows.js) calls `_appendLineageConnectionLines(svg, rects)` at its tail, exactly like ultracode's two layers, so all of them share ONE batched read→write reflow and the same `tab:<id>` rect cache. Geometry is pure and unit-tested in `computeLineagePath()` (constants.js): both endpoints live in one horizontal strip, so the subagent shape (tab-bottom → window-top) has nothing to aim at, and every pair gets a U-bridge HANGING BELOW the strip, anchored on both tabs' BOTTOM edges (dip scales with distance, plus a per-sibling step so several children of one parent nest instead of overprinting, plus the row offset when the strip has wrapped). ⚠️ **A wrapped strip used to get its own shape, and that shape was the bug** (fixed 2026-08-14): `tabs-two-rows`/`tabs-auto-wrap` put a parent on row 1 ~14px above its child on row 2, so the old parent-bottom → child-TOP bezier had 14px to bend in and drew a flat line inside the row gap, siblings overprinting. Hanging the control points below the LOWER row gives the wrapped case the same bracket as the flat one and deletes the branch. The same pass raised the dip clamp (44 → 104, 0.06 → 0.085/px) because a skill worker is appended to the END of the strip, where the old cap flattened an 800-1500px span into a straight thread across the terminal, and traded weight for a second, wider glow (2 → 2.5px, `4 4` → `5 5` dashes at `-20`, opacity .55 → .72 / .95 working) because the original styling vanished into terminal text at 1:1.
+**Rendering is an additional LAYER, not a second pass** (`session-lineage.js`, loadorder 15.6): `_updateConnectionLinesImmediate()` (subagent-windows.js) calls `_appendLineageConnectionLines(svg, rects)` at its tail, exactly like ultracode's two layers, so all of them share ONE batched read→write reflow and the same `tab:<id>` rect cache.
 
-⚠️ **Desktop only, for a z-index reason**: the overlay is `z-index: 999` and the desktop header is 100, so arcs paint OVER it — which is exactly what lets them touch tab bottoms. Under 1024px mobile.css makes the header `position: fixed; z-index: 1200` and would bury them, and the phone strip is a scroller where both endpoints are rarely on screen at once. Raising the SVG to ~1250 (above the fixed header, below modals at 1300) is the phase-2 option, and needs a real check against the mobile overview and the drawer.
+**Only the SELECTED tab's family is drawn** (2026-10-06): the family the active tab spawned, plus the family it was spawned into (its parent and siblings); a tab that is both a child and a parent shows both, in separate lanes. Nothing is drawn while a web tab holds the stage. Drawing every family at once is what the owner called "too confusing": one parent with ten children across a five-row wrapped strip drew ten glowing dashed beziers through every lower row's labels and into the terminal text. ⚠️ Because the drawing now depends on the selection, `_updateActiveTabImmediate()` redraws whenever any lineage exists (`_lineageTotalEdges > 0`), and the incremental tab render redraws on the same condition (a child's `parentSessionId` or working state can arrive there). `_lineageEdgeCount` counts what is DRAWN and still gates the strip-scroll redraw. ⚠️ **A selection keeps resizing tabs AFTER that redraw**: the active tab reveals its gear and close icons by transitioning their padding (~150ms), which can move tabs or re-wrap a row, so the strip's `transitionend` (size properties only: `width`, `max-width`, `padding*`) triggers one more coalesced redraw. Without it the trunk hung under the tab's old position (measured ~10px off, more after a re-wrap).
 
-⚠️ **`data-agent-id="lineage:<childId>"` is load-bearing**, not a label: `_applyLineEntrances()` queries paths by that attribute, so tagging them this way is the whole reason the arcs get the draw-in animation AND its negative-`animation-delay` resume across `svg.innerHTML = ''` with zero new animation code. ⚠️ `.session-tabs` is `overflow-x: auto`, so a tab scrolled out of the strip still HAS a rect — one lying over the logo or the header buttons; edges with an endpoint outside the strip are SKIPPED (clamping would point at a tab that is not there), and a passive `scroll` listener re-anchors the rest, since a scroll moves both endpoints without firing any render. The incremental tab render also redraws when `_lineageEdgeCount > 0`: a badge appearing widens a tab and shifts every tab after it. Setting: `sessionLineageLines`, per-device (in `displayKeys`, absent from the `.strict()` `SettingsUpdateSchema`), desktop default ON. Tests: `test/session-lineage-lines.test.ts` (geometry), `test/routes/session-routes-parent-lineage.test.ts` (resolution + reject paths).
+**Geometry is a tree routed through the gaps** (`computeLineageTree()` + `computeLineageRows()`, constants.js, pure and unit-tested): one rounded orthogonal tree per spawning tab. Every route starts at the PARENT's bottom-center and ends at one child's bottom-center, so a parent's routes share their first stretch exactly and overlay into one trunk with a branch per child; that is also what keeps a working child's dashes in phase with its siblings along the shared part. A route moves horizontally only inside a row gap (the gap under each endpoint's row, at the row's TALLEST tab, since the active tab is 2px taller) and vertically only along a tab's own stem or the SPINE, a channel left of every row that joins the gaps of different rows. In the vertical rail the same idea is one shared track down `--lineage-vertical-gutter`. `test/session-lineage-lines.test.ts` pins "never crosses a tab" as a property over a five-row fixture. ⚠️ **The room is reserved, not borrowed**: `.session-tabs.lineage-tree` (styles.css) adds bottom padding for the last row's gap, and on a wrapped strip a 12px row gap plus a 20px left channel for the spine. `_syncLineageGutter()` toggles it from the top of `updateTabOverflowMode()`, BEFORE the wrap is measured, and keys it on whether ANY family exists, never on the selection: the header's height is the terminal's height, so a class that followed the selection would resize the PTY on every tab switch. ⚠️ **Opacity lives on the family `<g class="lineage-family">`, not on the paths**: translucent paths overlapping along the trunk would stack into a brighter line than the branches. Working routes are appended first so an idle sibling's solid stroke covers the shared trunk. Style is deliberately quiet (1.5px, rounded, a 1px dark outline instead of the old double glow): the lines no longer cross text, so they no longer need a glow to survive it, and a dash now means "this child is working".
 
-Further detail (current geometry and colors, superseding the dip numbers above where they differ): ⚠️ **ONE shape, and the second one was the bug**: every pair (flat strip or wrapped) gets a U-bridge hanging below the strip, anchored on both tabs' BOTTOM edges. ⚠️ The dip is a **mis-tuned-in-both-directions corridor** (44px cap = straight thread at strip-wide spans, #285; 104px cap + full row offset = ~106px over-bow into the terminal, 2026-08-15): it now hangs from the **STRIP's bottom edge** (fallback: lower tab bottom), capped at 64px, with NO per-row offsets stacked on top — the strip-bottom baseline is also what keeps a row-1 pair's arc from drawing through row 2's tab labels.
+⚠️ **Desktop only, for a z-index reason**: the overlay is `z-index: 999` and the desktop header is 100, so the lines paint OVER it, which is exactly what lets them touch tab bottoms. Under 1024px mobile.css makes the header `position: fixed; z-index: 1200` and would bury them, and the phone strip is a scroller where both endpoints are rarely on screen at once. Raising the SVG to ~1250 (above the fixed header, below modals at 1300) is the phase-2 option, and needs a real check against the mobile overview and the drawer. The sidebar layout draws no lineage.
 
-⚠️ **Colors are keyed on the SPAWNING tab, not per child**: every arc leaving one tab is the same color however many workers it spawns, so the strip reads as "these five came from w1, those two came from w2" — per-child coloring gave one tab's own children a different color each, which is the distinction the colors exist to make. A child that spawns in turn is a parent in its own right and gets its own color for the arcs below it, so a chain changes color at each generation while each generation's fan-out stays uniform. Assignment cycles `CodemanLineage.COLORS` in first-seen order per parent id (first entry empty = the skin-tuned `--session-blue`, so the first spawning tab keeps it; the rest vivid fixed hexes), memoized rather than derived from draw index (the SVG is wiped and rebuilt constantly, so an index-based color would flicker), and set inline as `--lineage-color` so styles.css keeps owning opacity/glow/dash. `test/session-lineage-lines.test.ts` drives the real `_appendLineageConnectionLines()` and asserts the painted property, since testing the color function alone would pass just as happily with the child id passed back in.
+⚠️ **`data-agent-id="lineage:<childId>"` is load-bearing**, not a label: `_applyLineEntrances()` queries paths by that attribute (nested inside the family group is fine), so tagging them this way is the whole reason the lines get the draw-in animation AND its negative-`animation-delay` resume across `svg.innerHTML = ''` with zero new animation code. ⚠️ `.session-tabs` scrolls, so a tab scrolled out of the strip still HAS a rect, one lying over the logo or the header buttons; an endpoint outside the strip is SKIPPED (a child is left out, a parent drops its whole family), since clamping would point at a tab that is not there, and a passive `scroll` listener re-anchors the rest, since a scroll moves both endpoints without firing any render. Setting: `sessionLineageLines`, per-device (in `displayKeys`, absent from the `.strict()` `SettingsUpdateSchema`), desktop default ON. Tests: `test/session-lineage-lines.test.ts` (geometry, focus rule, routing room, colours), `test/routes/session-routes-parent-lineage.test.ts` (resolution + reject paths).
+
+History: before the tree, every pair got a U-bridge bezier hanging below the strip, and its dip was mis-tuned in both directions (a 44px cap flattened strip-wide spans into a straight thread, #285; a 104px cap plus the row offset bowed ~106px into the terminal, 2026-08-15). The tree removed the dip entirely.
+
+⚠️ **Colors are keyed on the SPAWNING tab, not per child**: every line leaving one tab is the same color however many workers it spawns, so the strip reads as "these five came from w1, those two came from w2"; per-child coloring gave one tab's own children a different color each, which is the distinction the colors exist to make. A child that spawns in turn is a parent in its own right and gets its own color for the lines below it, so a chain changes color at each generation while each generation's fan-out stays uniform. Assignment cycles `CodemanLineage.COLORS` in first-seen order per parent id (first entry empty = the skin-tuned `--session-blue`, so the first spawning tab keeps it; the rest vivid fixed hexes), memoized rather than derived from draw index (the SVG is wiped and rebuilt constantly, so an index-based color would flicker). ⚠️ The draw pass claims a color for EVERY family in strip order, drawn or not, so which family happens to be selected first never decides who gets the blue. Colors are set inline as `--lineage-color` so styles.css keeps owning weight and dash. `test/session-lineage-lines.test.ts` drives the real `_appendLineageConnectionLines()` and asserts the painted property, since testing the color function alone would pass just as happily with the child id passed back in.
 
 ### Auto-named sessions (first prompt → tab title)
 
@@ -771,7 +775,7 @@ Further detail: in the Settings section order, the version and the updater lead
 
 **The session list can render as the horizontal header strip (default) or as a collapsible left sidebar** — App Settings → Layout → Tabs → **Session List Layout** (`sessionListLayout: 'header' | 'sidebar'`, in the per-device `displayKeys` set, so it never syncs across devices; also in `SettingsUpdateSchema`, which is `.strict()` — without that entry the server 400s the ENTIRE settings PUT and every unrelated setting silently stops persisting). ⚠️ **There is exactly ONE `#sessionTabs` element and `applySessionListLayout()` RE-PARENTS it** between `#sessionTabsHost` (in `<header>`) and `#sessionSidebarList` (in the `<aside>`, a flex sibling of `.terminal-wrap` so the terminal shrinks and `terminal-ui.js`'s `ResizeObserver` refits xterm on its own). It must never be cloned or rebuilt: `app.$(id)` caches elements by id and NEVER invalidates, and `settings-ui.js` / `webview-tabs.js` resolve the same id independently, so a rebuilt container leaves every consumer writing into a detached orphan — silently, with no error. Everything else is CSS keyed off `html[data-session-list]` / `html[data-sidebar]`, both written by a pre-paint script in `<head>` so the loading skeleton already matches. Consequences: the renderers, drag/keyboard handlers, web tabs (`data-webview-id` rows stay in the same list, keeping the shared Alt+N numbering and the single-active-tab invariant) and the generated gesture bundle (`TAB_SELECTOR`/`DOCK_SELECTOR` match on class names that are unchanged) all need **zero** edits.
 
-⚠️ Collapsed means **different things per viewport**: at 1024px and up the sidebar keeps a 44px icon rail so the ambient signal (status dot, task/subagent/ultracode badges) survives — the Alt+N number, the name/folder and the `sh`/`oc`/`cx`/`gm` mode chip do NOT, because 44px minus paddings and borders is ~34px of content box and the chip lives inside `.tab-info`; below 1024px `mobile.css` turns the sidebar into an off-canvas overlay where collapsed == drawer closed (mirrored into an `.open` class plus `inert`/`aria-hidden`, since `translateX(-100%)` alone leaves every row in the Tab order), it defaults to CLOSED when the user has made no choice, and picking a session or web tab dismisses it. ⚠️ **That 1024px breakpoint is the only handheld test the sidebar may use** (`_isSessionSidebarOverlay()`, mirrored in the pre-paint script): `MobileDetection.getDeviceType()` calls everything from 768px up `'desktop'`, so using it gave 768-1023px the overlay CSS with docked-sidebar logic — drawer opening itself on load, immune to selection and Escape. The toggle chord (default Alt+B) also needs its gate in `terminal-ui.js`'s `attachCustomKeyEventHandler`, or `preventDefault()` in the capture handler still lets xterm write ESC b into the live PTY (same trap as COD-153). The sidebar filter only applies while its input is on screen — `applySidebarFilter()` strips the class in the header strip, the collapsed rail and the closed drawer, because a filter with no reachable control hides sessions permanently. Collapse state lives in its OWN `codeman-sidebar-collapsed` key, **not** in the settings blob — `saveAppSettings()` rebuilds that blob from DOM controls, so a key without a control is wiped on every Save. Solo (`/session/:id`) windows never get a sidebar (three guards: `getSessionListLayout()`, the pre-paint script, and `body.solo-mode`), because `#sessionTabs` parked in a `display:none` subtree measures 0/0 for tab overflow and inline rename. The sidebar CSS block sits at the END of `styles.css`, **after** the `html:not([data-skin="og"])` nesting block, and is layout-only — any colour on `.session-tab` there would render correctly on the `og` skin only. Same for the `mobile.css` block: it must stay at the end of the file or the earlier compact-strip rules clip the list to a 36px sliver. Two surfaces DEFER to the sidebar rather than adapt: **lineage arcs are skipped** in sidebar layout (`_appendLineageConnectionLines` early-returns — `computeLineagePath()`'s whole geometry hangs a U-bridge from the horizontal STRIP's bottom edge, so against a vertical list every arc would loop to the foot of the sidebar; a sideways lineage shape needs its own visual tuning, it is not a by-product of re-parenting), and the **desktop home tab rail** (`shouldShowHomeSessions()`) stays hidden while the sidebar is active, because both dock the session list flush left and the rail would render the same list next to it, z-ordered UNDER it. The subagent/ultracode connectors DO adapt (`_tabAnchor()`/`_tabConnectorPath()` in app.js: right-edge anchor, horizontal bezier), and the lineage strip-scroll listener redraws them on the sidebar's vertical scroll. `_scrollActiveTabIntoView()` owns active-row reveal on BOTH axes: sidebar mode branches to `scrollIntoView({block:'nearest'})` because the horizontal `computeTabScrollLeft` math no-ops against a vertical scroller, and `_fullRenderSessionTabs()` restores `scrollTop` alongside the #257 `scrollLeft` restore or ambient rebuilds yank a mid-scroll sidebar back to the top. Tests: `test/session-list-layout.test.ts`.
+⚠️ Collapsed means **different things per viewport**: at 1024px and up the sidebar keeps a 44px icon rail so the ambient signal (status dot, task/subagent/ultracode badges) survives — the Alt+N number, the name/folder and the `sh`/`oc`/`cx`/`gm` mode chip do NOT, because 44px minus paddings and borders is ~34px of content box and the chip lives inside `.tab-info`; below 1024px `mobile.css` turns the sidebar into an off-canvas overlay where collapsed == drawer closed (mirrored into an `.open` class plus `inert`/`aria-hidden`, since `translateX(-100%)` alone leaves every row in the Tab order), it defaults to CLOSED when the user has made no choice, and picking a session or web tab dismisses it. ⚠️ **That 1024px breakpoint is the only handheld test the sidebar may use** (`_isSessionSidebarOverlay()`, mirrored in the pre-paint script): `MobileDetection.getDeviceType()` calls everything from 768px up `'desktop'`, so using it gave 768-1023px the overlay CSS with docked-sidebar logic — drawer opening itself on load, immune to selection and Escape. The toggle chord (default Alt+B) also needs its gate in `terminal-ui.js`'s `attachCustomKeyEventHandler`, or `preventDefault()` in the capture handler still lets xterm write ESC b into the live PTY (same trap as COD-153). The sidebar filter only applies while its input is on screen — `applySidebarFilter()` strips the class in the header strip, the collapsed rail and the closed drawer, because a filter with no reachable control hides sessions permanently. Collapse state lives in its OWN `codeman-sidebar-collapsed` key, **not** in the settings blob — `saveAppSettings()` rebuilds that blob from DOM controls, so a key without a control is wiped on every Save. Solo (`/session/:id`) windows never get a sidebar (three guards: `getSessionListLayout()`, the pre-paint script, and `body.solo-mode`), because `#sessionTabs` parked in a `display:none` subtree measures 0/0 for tab overflow and inline rename. The sidebar CSS block sits at the END of `styles.css`, **after** the `html:not([data-skin="og"])` nesting block, and is layout-only — any colour on `.session-tab` there would render correctly on the `og` skin only. Same for the `mobile.css` block: it must stay at the end of the file or the earlier compact-strip rules clip the list to a 36px sliver. Two surfaces DEFER to the sidebar rather than adapt: **lineage lines are skipped** in sidebar layout (`_appendLineageConnectionLines` early-returns: `computeLineageTree()` routes through a horizontal strip's reserved row gaps or the vertical rail's reserved `--lineage-vertical-gutter`, and the sidebar has neither; a sidebar lineage shape needs its own visual tuning, it is not a by-product of re-parenting), and the **desktop home tab rail** (`shouldShowHomeSessions()`) stays hidden while the sidebar is active, because both dock the session list flush left and the rail would render the same list next to it, z-ordered UNDER it. The subagent/ultracode connectors DO adapt (`_tabAnchor()`/`_tabConnectorPath()` in app.js: right-edge anchor, horizontal bezier), and the lineage strip-scroll listener redraws them on the sidebar's vertical scroll. `_scrollActiveTabIntoView()` owns active-row reveal on BOTH axes: sidebar mode branches to `scrollIntoView({block:'nearest'})` because the horizontal `computeTabScrollLeft` math no-ops against a vertical scroller, and `_fullRenderSessionTabs()` restores `scrollTop` alongside the #257 `scrollLeft` restore or ambient rebuilds yank a mid-scroll sidebar back to the top. Tests: `test/session-list-layout.test.ts`.
 
 Further detail: with many sessions the horizontal strip stops being scannable, which is why the list can move into the vertical `<aside>` with a filter box and a live count, collapsible to a 44px rail (`--sidebar-width` 260 / `--sidebar-width-collapsed` 44) via **Alt+B** (`toggleSessionSidebar`; Alt, not Ctrl+B, which must reach tmux/readline in the terminal). The setting lives in App Settings → Appearance → Tabs. There is a THIRD host for `#sessionTabs` besides `#sessionTabsHost` and `#sessionSidebarList`: `#tabRail`, the vertical rail. Exactly TWO functions reparent it and they must run in this order: `applySessionListLayout()` first (sidebar wins), then `applyTabOrientation()` (settings-ui.js), which moves the tabs into `#tabRail` only when the sidebar does not own them. ⚠️ `applySessionListLayout()` sets `data-session-list` / `data-sidebar` on `<html>` and must run BEFORE `applyTabWrapSettings()`, which is the one owner of `tabs-two-rows`/`tabs-show-folder` and reads those attributes.
 

docs/wiki/Driving-Codeman-From-An-Agent.md

@@ -189,7 +189,7 @@ followed by a wait races, and reports the previous turn's state.
 ## Lineage
 
 A create request can name the session that spawned it, through a body field or a header, and
-the dashboard then draws a lineage arc from parent to child. The skill sets it automatically.
+the dashboard then draws a lineage line from parent to child. The skill sets it automatically.
 
 It is resolved rather than trusted: an unresolvable parent is dropped silently rather than
 failing the spawn, because a cosmetic field must never break a worker.

docs/wiki/Mobile-Guide.md

@@ -158,7 +158,7 @@ enough to fix a typo an agent introduced while you are away from your desk.
   enforces it.
 - The Approvals bell. Phones get the NEEDS YOU strips on the home screen instead.
 - The desktop home tab rail, which needs a wide window.
-- Lineage arcs, which are a desktop overlay.
+- Lineage lines, which are a desktop overlay.
 
 ## Gotchas
 

docs/wiki/Settings-Reference.md

@@ -89,7 +89,7 @@ every session or only the active tab.
 | Vertical Rail Order    | *By activity* (default) sorts the rail the way the home screens are sorted; *Manual* keeps your tab order and drag-reordering. |
 | Tall Tabs              | Taller tab strip.                                                                          |
 | Pop-out Button on Tabs | Adds the detach control to tabs, with a per-tab override.                                  |
-| Spawn Lineage Lines    | Arcs from a parent tab to sessions it spawned. Desktop only, on by default.                |
+| Spawn Lineage Lines    | Lines from the selected tab to the sessions it spawned, and to the one that spawned it. Desktop only, on by default. |
 | Auto-name Sessions     | Titles a new tab after its first prompt, keeping the case prefix (`w3-myapp: fix the login redirect`). Synced, off by default. See [The Dashboard](The-Dashboard#automatic-session-names). |
 | Overview Home Screen   | The phone home screen. On by default.                                                      |
 

docs/wiki/The-Dashboard.md

@@ -84,13 +84,17 @@ title is derived locally from the prompt's first sentence; no text leaves the ma
 On phones the strip scrolls horizontally instead of wrapping, and the active tab is always
 scrolled into view. It is not reordered to the front, so the `Alt+N` numbering stays stable.
 
-### Lineage arcs
+### Lineage lines
 
-When one session spawns another (an agent starting a worker through the API), Codeman draws
-a coloured arc under the strip connecting parent to child, with one colour per child. It is
-how a fan-out of eight workers stays readable.
+When one session spawns another (an agent starting a worker through the API), selecting
+either tab draws its family: lines from the parent to each child, in the parent's colour,
+routed through the gaps between tab rows so they never cover a tab or the terminal. A dashed
+branch means that child is working. It is how a fan-out of eight workers stays readable.
 
-Desktop only, and on by default. Turn it off in **App Settings → Appearance**. Arcs are
+While any tab has spawned another, the strip keeps a little extra room between rows for the
+lines, so switching tabs never changes the header height.
+
+Desktop only, and on by default. Turn it off in **App Settings → Appearance**. Lines are
 skipped for tabs scrolled out of the strip.
 
 ## Header controls

docs/wiki/Watching-Agents-Work.md

@@ -22,13 +22,17 @@ transcript: what it was asked to do, what it is doing, and what it returned.
 This is the feature that makes a fan-out legible. Without it, a lead session that spawned
 eight workers looks like a stalled terminal for several minutes.
 
-## Session lineage arcs
+## Session lineage lines
 
-The tab strip draws a coloured arc from a parent tab to any tab it spawned, one colour per
-child. That covers the other direction of fan-out: not subagents inside one session, but
-whole sessions started by an agent through the API.
+Select a tab and the tab strip draws lines from it to every tab it spawned, and to the tab
+that spawned it (with its siblings). That covers the other direction of fan-out: not
+subagents inside one session, but whole sessions started by an agent through the API.
 
-Desktop only, on by default, and toggled in **App Settings → Appearance**. Arcs are skipped
+The lines form one tree per spawning tab, in that tab's colour, and run only through the
+gaps between tab rows, so they never cover a tab name or the terminal. A dashed branch
+means that child is working. Tabs with no lineage draw nothing.
+
+Desktop only, on by default, and toggled in **App Settings → Appearance**. Lines are skipped
 for tabs scrolled out of view.
 
 See [Driving Codeman From An Agent](Driving-Codeman-From-An-Agent) for the spawning side.